The major focus of this project is the development of novel methodologies for the detection and estimation of gene-environment (G E) interactions for complex diseases. Recent advances in genetic studies have success- fully identified genetic variants that are associated with complex diseases such as cancer, heart disease and others. To further understand disease etiology, it is important to study the interplay between genetic and environ- mental risk factors. An important challenge to studying gene-environment interactions comes from the difficulty in environmental exposure assessments. Most environmental risk factors, such as diet, physical activity and air pollution, are measured imprecisely and self-reported diet or physical activity may suffer from substantial sys- tematic bias. Many environmental exposures are time-varying and their effects on health outcomes can be rather complicated. Existing statistical methods that deal with these types of complex environmental assessments have focused on main effects, and little has been developed for G E interactions. With these practical challenges in mind, our goal is to develop statistical methodologies that account for mea- surement error and time-varying exposures for GE interactions. In the presence of environmental measurement error, we will first evaluate the validity of na1ve tests that ignore measurement error. We then extend regression calibration methods to interaction models for both exposures with classical measurement error and measure- ments subject to systematic bias. Typical examples for the latter include diet and physical activity self-report assessments. The proposed calibrated analyses are expected to be more powerful for testing GE interactions. For time-varying environmental factors such as air pollution, we propose novel functional data analysis methods that allow flexible modeling of environmental main effect and G E interactions. The functional model framework utilizes temporal patterns of exposures and can potentially improve power to detect G E interactions. The proposed methodological research is motivated by scientific problems from large-scale epidemiological studies (e.g., the Women's Heath Initiative) and will be directly applied to these projects.